Wave energy is among the many alternative energy production methods that have been the subject of intensified research in recent years. A concern about diminishing fossil fuel supplies, as well as global climate change, has added impetus to this activity, resulting in many successful demonstrations of wave energy capture (WEC).
One area where WEC may be employed is in powering unmanned maritime systems, including distributed sensing systems, unmanned maritime vehicles (UMVs) (both surface and submersible), and near-shore logistics systems. These systems are heavily influenced by three primary criteria: mission capability, endurance, and available power. Increases in capability and endurance create a demand for more power, and thus any technology that increases available power is desirable. To date, energy sources include fossil fuels or other energetic chemical fuels (hydrogen, ammonia, etc.), metal-water reactions, batteries, and photovoltaics. Chemical fuels require large volume and increase the mass of the vessel early in the mission, followed by a need to ballast with deadweight later on in the mission, which is detrimental to fuel efficiency. Primary and secondary storage batteries are limited in their energy density and there is no large leap in capacity envisioned. Photovoltaics provide some relief, but require a proportional amount of surface area, work optimally only during clear daytime conditions, and are affected by latitude and season.
An available source of energy for marine systems comes from the seas they encounter, either while cruising, station keeping, or drifting. Ocean waves and swells are created by a variety of physical processes. The ocean waves and swells of interest for the embodiments described herein are generally those generated by wind forcing, but can be from any forcing mechanism producing the amplitude (height) necessary to allow harvesting. Waves differ from one another and from time to time not only in terms of their height, as measured from peak to trough, but also by their shape and period (length). Wave shapes run in a continuum ranging from long sinusoidal swells to steep and trochoidal with well-defined peaks. The average kinetic energy of waves is significant, but a practical means of harnessing it aboard a free-floating vessel, other than for very low-speed propulsion (e.g., flapping fins), has not been realized. The devices described herein are low in both dry mass and volume, able to be deployed and retrieved repeatedly and on demand, and able to harvest enough ocean energy to support continuous operations for relatively long periods of time (e.g., months).
Wave kinetic energy is manifested by the rising and falling of the volume of water contained in the wave as it propagates through the ocean. In theory, a vessel should be able to harvest some portion of the wave energy impinging upon it. To do this, the wave must be absorbed without being simply reflected. Harvesting ocean wave energy requires that some means be used to cause the wave to exert a force against some type of mechanical actuator, which can perform useful work. In most cases, the end work product is electrical current, produced by a generator (or alternator).
Conventional WEC devices require moving parts, are exposed to the biological and chemical processes of marine fouling, and are exposed to extremes of mechanical stress. These factors, when taken together, pose numerous engineering challenges and unique solutions. Wave energy as a viable commercial power source will require large numbers of highly reliable devices to be deployed and maintained in a hostile environment at a minimum cost. For naval applications, there are transition opportunities for wave energy that are cost-effective, notably as a power source for buoys and UUVs and other remote applications where energy storage density limits endurance.
To understand why wave energy should be considered as an attractive source of power for ocean vehicles, a comparison may be made to other forms of environmental energy, namely wind and solar. These forms of energy can be expressed in terms of their density per square meter as a raw value in Watts. An alternative energy capture device converts some fraction of this raw energy into harvested output. The captured energy is ultimately used directly, stored (usually in secondary batteries) or shed depending on demand.
The raw energy of wind is a function of the density of air and its velocity, in the general formP(wind)=0.5*ρAV3 where    P is the power in Watts;    ρ is the density of air (about 1.2 kg/m3);    A is the area in square meters;    and V is velocity in meters/sec.
Most wind energy devices operate at 25-45% efficiency. The theoretical maximum, known as Betz's law, is 59.3%. However, wind devices are not attractive as sources of energy for many offshore missions due to high visibility, vulnerability to wave damage, variability of winds, and potential hazards to humans and marine life.
Solar energy, at noon at the equator, provides total energy flux of about 1300 Watts/m2. The overall clear-sky daylight power level depends on the angle of the sun relative to that of the collector, expressed asP(solar)=1300*sin θ,    where    P is power in Watts, and    θ is the sun angle, with 90° being directly overhead.
Solar angle changes with time of day, season, and vessel motion. Typical solar panels operate at 15-30% efficiency under ideal conditions. Any type of cloud cover, precipitation, and obscuration greatly reduces the instantaneous solar irradiance value. In addition, solar collector efficiency can be rapidly degraded in the marine environment due to biological fouling (e.g., birds or algae). At the equator, the RMS value of cloudless daytime solar irradiance will be 800 Watts per square meter. Therefore, one square meter of solar panels operating at 25% efficiency at the equator delivers 2400 Watt-hours of total power per day—a mean power of 100 Watts, and a storage requirement of 1200 watt-hours (12 kg of lithium-ion batteries) for continuous nighttime operation. Installation constraints can also significantly reduce solar efficiency.
Wave energy is the amount of energy present in the rising and falling water mass of passing waves. The available power isP(wave)=0.5*T*h2.    where    P is power in    Kilowatts,    T is the wave period in seconds, and    h is the height of the wave (trough to crest) in meters.
For example, a wave 1 meter in height having a period of 5 seconds contains 2.5 kilowatts of power per linear meter of wave front. This wave energy can propagate for very long distances before slowly dissipating in the open sea or against some object such as a coastline. By comparison, wave energy is more ubiquitous and dependable than wind energy, because WEC devices can operate using swells and are not reliant on wind driven seas. Wave energy devices typically operate at 10-25% efficiency. Thus, during a 24-hour period in a 1-meter, 5-second sea, using a vessel hull of 1 square meter, a wave energy conversion device operating at 10% efficiency delivers 6000 Watt-hours of total energy—an output power of 250 Watts, day and night. As a general rule of thumb, wave power per square meter of sea surface becomes greater than solar (neglecting clouds and latitude) when the wave height exceeds about 0.5 m. Statistically, global wave heights average greater than 0.5 m, but vary considerably with ocean and region.
One important commonality shared by wind and wave energy is that they do not have an upper bound in the same way that solar does. As wind speed increases, the energy impinging on a collection device increases with the cube of the wind velocity, or a factor of eight for each doubling in speed. Wave energy increases by a factor of about 32 for each doubling of wave period. The importance of this is that wind and wave collectors must be designed to operate under some minimum conditions and be able to safely shed energy to avoid destruction above some upper limit.
Because solar and wave energy are not mutually exclusive, it is possible that both sources may be utilized on the same vessel. Thus, on a sunny day, under the conditions described above a vessel could have 7440 Watt-hours of energy available for real time work and battery charging; enough for significant mobility and payload operations.
Critical insights on how to best harness wave energy can be gained by considering an idealized sinusoidal sea. The well-known form of the amplitude of the free surface sine wave is:Y=h*sin(bt)2     where    Y=y-axis position of the wave surface at time t    h=height of the wave (divided by 2 because h is conventionally the trough to crest distance)    b=2*π/T, (T being the period in seconds)    t=time
Vertical velocity is the first derivative:Y′=h*b*cos(bt)2 
Devices that attempt to harvest wave energy by utilizing drag via the use of underwater plates must obey the drag force equation:F=0.5ρA(Y′)2*C,     where    ρ=density of seawater (˜1030 kg/m3)    A=the Area of the plate in square meters, and    C=a drag coefficient for the shape (assume 1 for a flat plate).
Due to the presence of velocity (Y′) squared in this equation, small changes in velocity lead to large changes in force. This fact, coupled with the unbounded nature of velocity as a function of wave height, means that the forces acting on a plate of a given size (area) vary greatly. A plate with sufficient area to harvest energy from small waves, and hence small velocities, must be large in area. This has major implications when it comes to the design of a practical velocity-driven wave energy capture device.
Vertical acceleration is the second derivative:
            Y      ″        =                  h        2            *              b        2            *              [                  -                      sin            ⁡                          (              bt              )                                      ]                                V        MAX            =                        Y          MAX          ′                =                              h            2                    *          b                      ,                  ⁢    and        Max_Accel    =                  Y        MAX        ″            =                                    h            2                    *                      b            2                          =                              Y            ′                    *                      b            .                              
Note that when T is small, b becomes larger. FIG. 1 shows these time series for sinusoidal waves of two different heights. As used herein, waves have the same “shape” if their ratio of height to wavelength is the same. Wavelength of an ocean gravity wave is given by:
  L  =            gT                                        ⁢        2                    2      ⁢      π      Therefore, if constant h/L defines waves of the same shape, so does constant h/T2.
Waves of the same shape have very similar acceleration values (exactly equal in the case of sinusoidal waves). For example, for a 1-meter wave of period 5 seconds,L=39 mVMax=0.63 m/s2, andMax_Accel=VMAX*b=0.79 m/s2.
A 0.2-meter wave of the same shape has T=2.23 sec andL=7.8 mVMax=0.28 m/s, and againMax_Accel=VMAX*b=0.79/s2.
A wave's vertical acceleration is more tightly bounded than velocity, therefore making it more straightforward to design devices to efficiently exploit acceleration than velocity. Wave shapes will vary but are bounded by h/L= 1/7, at which point waves are generally observed to break. A sinusoidal wave of this limiting shape will have Max_Accel=4.4 m/s2. This is important to present embodiments when wind is local, as short period steep waves will produce larger acceleration forces.
The majority of existing WEC devices cannot function without mooring to provide a reaction force. WEC devices that can function while drifting can be categorized in terms of their wave coupling modality: flexural; oscillatory/resonant; angle rate and surge; and pure heave. Examples include the Pelamis system (www.pelamiswave.com), which is a very large flexural device. In this system, a spatially differentiated heave causes a long chain of spars to deflect, and energy is extracted at the spar connection points. A disadvantage of this device is that it is sensitive to orientation—it must be pointed into the seas to function. It would be inefficient in a multidirectional sea, although such seas are common. Some design studies have been done on a two-dimensional flexural system, the Wave Carpet, designed to overcome this disadvantage. See “The Dynamics of Wave Carpet, A Novel Deep Water Wave Energy Design,” Oceans 2003 Proceedings, vol. 4, pp. 2288-2293.1). The principal characteristic of flexural systems is their very large size, because to work efficiently, their length scale must be comparable to the wavelengths of ocean gravity waves. Also, because ocean wave height and length are related, it is difficult to dynamically tune such devices.
An oscillatory water column device is described in Jin-Ha Kim, et al., “An Experimental Study on the Reverse Wave Drift Force of a BBDB Type OWC Wave Energy Device,” Proceedings of The Seventh (2006) ISOPE Pacific/Asia Offshore Mechanics Symposium, p. 237 and in http://www.gizmag.com/wave-power-owc/11122/. Resonant devices can be relatively small, but they require compromise between generation efficiency, which is highest in a narrow resonance band, and wave coupling efficiency, which demands a broad resonance to couple to broad wave spectra.
Other devices include angle rate/surge WEC devices such as a working mass WEC which develops less power per unit of deadweight mass, but can have all of its working parts sealed and not exposed to the marine environment, potentially lasting for several years without maintenance. Exemplary devices are described in U.S. Pat. No. 7,629,704. The devices include a heavy eccentric mass mounted on a vertical shaft. As the buoy pitches, rolls, and is pushed by surge motions, the mass responds inertially and rotates around the shaft, converting wave motion into rotational mechanical movement, and through a transmission to turn a generator. The device requires large working mass and is highly sensitive to chaotic inputs. A disadvantage of angle-rate and surge devices in general is that the power-to-mass ratio is relatively low.
In an exemplary non-resonant device, the differential motion of a spar and a broad float to move a magnet within a linear generator. Simplicity of design is an advantage, but disadvantages include: relatively low power-to-weight ratio; very large underwater profile, complicating deployment and repositioning; and relatively large above water protrusion, increasing its observability.
There is a need for small-scale, limited production, non-mooring WEC devices capable of supplying power to a wide range of applications, including, for example, all-electric UMVs.